Smoke might also come from wires supplying power to the starter. Check these also to make sure none of them is burnt, has broken insulation etc. Your starter will most likely be dead by now, but you might also have damaged something in the electrical installation. The installation is not supposed to handle such large current for such a long time.
As for the starter I would recommend buying original Toyota part, the whole thing basically, including the switch-box etc. Once you get it you could try installing it yourself. There are quite few descriptions concerning rebuilding contacts (the click problem) where you should be able to find detailed info on how to remove the starter unit (should be just 2 cables and 2 bolts, somewhat hard to get at though).
Check the "How to replace starter contacts" thread in HardCore tech/competition
http://www.toyotanation.com/forum/t19221.html
If replacing the starter doesn't help you'll probably have to check your elctrical installation.
Good luck, hope you won't need to spend a fortune on all that.